It is proved that any optimal backbone configuration must correspond to a capacity-maximizing Voronoi tessellation of the network region, and this can be efficiently approximated by a centroidal Voronoi tessellation via Lloyd's algorithm, with backbone nodes connected according to a Delaunay triangulation.
Abstract
Free-space quantum communication provides a flexible complement to fiber-based quantum networks, but its point-to-point capacity is fundamentally limited by diffraction, atmospheric extinction and beam wandering induced by turbulence. In this work, we study the end-to-end performance of large-scale free-space quantum networks connecting randomly distributed fixed or mobile users, modelled as Waxman random graphs. We derive the mean network capacity, edge consumption and connectivity phase transitions for both single-path and multi-path (flooding) routing. We also study router-centered star networks, deriving the full distribution of end-to-end capacities as a function of the router's coverage radius. We then consider how performance may be improved by reinforcing free-space networks with a small number of optimally placed fiber-based backbone nodes. We prove that any optimal backbone configuration must correspond to a capacity-maximizing Voronoi tessellation of the network region, and show that this can be efficiently approximated by a centroidal Voronoi tessellation via Lloyd's algorithm, with backbone nodes connected according to a Delaunay triangulation. Numerical results show that even a modest number of backbone nodes substantially improves end-to-end capacity and reduces edge consumption for both mobile and fixed users.
As practical quantum networks approach large-scale deployment, the need for efficient user-to-user frequency allocation is increasing, yet current approaches only provide partial solutions to the routing and spectrum allocation problem for an arbitrary quantum network. We address this challenge for repeater-less flex-grid quantum networks based on hyperentangled photons using an efficient three-stage pipeline combining leading tools in classical networking with recent advances in numerical optimization. First, double instantiations of Yen's algorithm obtain low-loss route candidates between each pair of users and the entanglement sources. Second, the advanced process optimizer (APOPT) obtains frequency channel allocations that maximize distribution rates under fidelity constraints. Finally, the constraint programming solver using satisfiability methods (CP-SAT) assigns specific frequency bins to each link, ensuring that there is no contention between frequencies from different sources. We numerically demonstrate this approach on a representative ring network and a Manhattan incumbent local exchange carrier topology, realizing significant improvements over prior genetic algorithm approaches in speed, accuracy, and scalability. Overall, this pipeline provides an efficient heuristic workflow for optimizing broadband entanglement distribution, applicable to arbitrarily connected quantum networks integrated within the existing lightwave infrastructure.
Zachary Goisman, M. L. Stevens, Maxwell Goisman et al.· 0 citations
We show that entanglement-generation speed across a fixed network interface is governed by two distinct resources: the entangling capacity of the interface itself and the ability of the surrounding architecture to replenish it with fresh degrees of freedom. For fermionic Gaussian dynamics, we derive the coefficient-sharp bound $\sum_k|\dot\theta_k|\leq\frac12\|K_{AB}\|_*$ on the collective speed of the canonical entanglement angles. Explicit Ising-chain rematching trajectories saturate this bound, thereby certifying exact minimum interaction times under the stated control model. Beyond the Gaussian setting, exhaustive optimization of the complete $N=8$ tree--tree family shows that, at fixed interface capacity, first-layer entanglement, connectedness, and edge budget, the saturation depth is exactly classified by rooted architecture. With higher-resolution $x$-only control, variational entanglement-enhancing-field (VEEF) optimization reaches the numerically resolved fast-$X$ optimum in a two-channel benchmark. Across all 21 symmetry-reduced rooted orbits, a pre-specified two-time VEEF growth diagnostic recovers the complete replenishment partition directly from optimized dynamics. Interface capacity therefore sets how much entangling flux is available, whereas architecture determines whether fresh degrees of freedom can continually replenish the interface and sustain repeated use of that capacity.
Adding links generally improves classical transport by increasing the number of available paths. We show that coherent quantum transport can display the opposite behavior. Using continuous-time quantum walks on a percolated hierarchical small-world network, we identify a coherent overconnectivity penalty: root-to-boundary transport is maximized at intermediate bond probability and decreases as the network approaches full connectivity. The effect is quantified by the final-layer limiting probability $\chi_N$ and by the penalty $P_Q=1-\chi_N(p=1)/\max_p\chi_N(p)$, which measures the loss caused by making the architecture fully connected. The optimum results from a competition between shortcut-assisted spreading and interference-induced intra-layer recirculation. Spectral analysis shows that bond dilution creates motif-induced degeneracies and reorganizes the eigenstates connecting the root to the outermost layer. A comparison with dephased and classical transport shows that the non-monotonic landscape is not a purely geometrical percolation effect, but a coherent architecture-dependent phenomenon. These results provide a design principle for coherent transport in disordered photonic and quantum-network architectures.
Miquéias J. Cirino, Marcos César de Oliveira· 0 citations
In this study, for the first time, a novel routing and purification approach for quantum networks is presented, using the end-to-end (E2E) relative entropy of coherence (REC) together with E2E fidelity to determine the purification level and the feasibility of candidate paths.
H. S. D. Tunç, Joy Halder, Azita Hajizade et al.· Scientific Reports· 0 citations
The realization of large-scale quantum networks requires more than advances in quantum repeaters, memories, and processors, it requires a framework explaining how heterogeneous quantum technologies evolve from isolated deployments into interconnected infrastructures. While the classical Internet evolved under strong utility incentives associated with resource sharing and communication demands, quantum networking currently lacks dominant applications capable of generating comparable incentives. As a consequence, contemporary quantum networks are largely formed through technology-driven decisions motivated by technical feasibility, experimental validation, and expected future value. This work argues that the absence of utility-driven network formation is not solely a consequence of immature applications, but also of insufficient abstraction. In particular, heterogeneous quantum platforms remain tightly coupled to the functionalities they provide, preventing the definition of technology-independent utility functions. A hierarchical architecture consisting of Physical Platforms (PP), Functionalities (F), Services (S), Applications (A), and Use-Cases (UC) is proposed, together with the argument that quantum interconnects constitute the enabling technology required to decouple physical implementations from network functionalities. Such decoupling permits the definition of utility functions at the functionality level and establishes the conditions under which strategic (agent-based) network formation becomes applicable. Quantum interconnects should therefore be viewed not only as interoperability devices, but also as fundamental enablers of strategic quantum network evolution.
Quantum Error Correction~(QEC)-protected direct transmission is a fundamental approach to preserve fragile quantum states while they are physically forwarded across noisy quantum networks. When a logical qubit traverses multiple hops, selected QEC-capable nodes may recover the encoded state before it continues along the route. The feasibility and cost of the final transmission strategy therefore depend on how we jointly choose the path, the recovery locations, and the protection schemes. In this paper, we formulate and analyze a cross-layer spatio-temporal path optimization problem for block-style stabilizer-code-protected direct transmission. Our main results include fixed-scheme and flexible-scheme single-flow routing algorithms, as well as a multi-flow routing algorithm. The framework developed in this paper can serve as an algorithmic building block for QEC-aware routing under logical-error and logical-lifetime constraints. Simulations show that it reduces single-flow average routing cost by approximately 25--30\% over Decode-Always and lowers multi-flow throughput-normalized congestion by approximately 28--31\% over Greedy-Assignment.
Yuanbo Zhang, Qianfan Wang, Yangmin Zhao et al.· 0 citations